Question

find the quadratic polynomial whose sum and product of the zeros are - 3 and 2 respectively.​

Answer 1

Answer:

$\alpha + \beta = - 3 \\ \alpha \beta = 2$

$\frac{ - b}{a} = \frac{ - 3}{1} = 3$

$\frac{c}{a} = \frac{2}{1} = 2$

$a = 1 \\ b = 3 \\ c = 2$

Polynomial is:

$k ({x}^{2} + 3x + 2 = 0)$

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Answer 2

Answer:

${x}^{2} + 3x + 2$

Step-by-step explanation:

$\alpha + \beta = - 3 \\ \geqslant \alpha \times \beta = 2 \\ \geqslant by \: formula \\ \geqslant {x }^{2} - ( \alpha + \beta )x + \alpha \beta \\ \geqslant {x}^{2} - ( - 3)x + 2 \\ \geqslant {x}^{2} + 3x + 2$

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